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Journal of Applied Mathematics
Volume 2013, Article ID 518269, 8 pages
http://dx.doi.org/10.1155/2013/518269
Research Article

Sensitivity Analysis of the Matrix Equation from Interpolation Problems

1School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, China
2School of Mathematics, Shandong University, Jinan 250100, China

Received 22 July 2013; Accepted 27 September 2013

Academic Editor: Carlos J. S. Alves

Copyright © 2013 Jing Li and Yuhai Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies the sensitivity analysis of a nonlinear matrix equation connected to interpolation problems. The backward error estimates of an approximate solution to the equation are derived. A residual bound of an approximate solution to the equation is obtained. A perturbation bound for the unique solution to the equation is evaluated. This perturbation bound is independent of the exact solution of this equation. The theoretical results are illustrated by numerical examples.